Large deviation principle for stochastic evolution equations

Summary The large deviation principle obtained by Freidlin and Wentzell for measures associated with finite-dimensional diffusions is extended to measures given by stochastic evolution equations with non-additive random perturbations. The proof of the main result is adopted from the Priouret paper concerning finite-dimensional diffusions. Exponential tail estimates for infinite-dimensional stochastic convolutions are used as main tools.     

On completely nonmeasurable unions

Assume that there is no quasi-measurable cardinal not greater than 2^ω . We show that for a c. c. c. σ -ideal 𝕀 with a Borel base of subsets of an uncountable Polish space, if 𝒜 is a point-finite family of subsets from 𝕀, then there is a subfamily of 𝒜 whose union is completely nonmeasurable, i.e. its intersection with every non-small Borel set does not belong to the σ -field generated by Borel sets and the ideal 𝕀. This result is a generalization of the Four Poles Theorem (see [1]) and a result from [3]. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Group topologies coarser than the Isbell topology

The Isbell, compact-open and point-open topologies on the set C(X,R) of continuous real-valued maps can be represented as the dual topologies with respect to some collections α(X) of compact families of open subsets of a topological space X. Those α(X) for which addition is jointly continuous at the zero function in Cα(X,R) are characterized, and sufficient conditions for translations to be continuous are found. As a result, collections α(X) for which Cα(X,R) is a topological vector space are defined canonically. The Isbell topology coincides with this vector space topology if and only if X is infraconsonant. Examples based on measure theoretic methods, that Cα(X,R) can be strictly finer than the compact-open topology, are given. To our knowledge, this is the first example of a splitting group topology strictly finer than the compact-open topology.     

A novel approach to the rapid determination of amoxicillin in human plasma by solid phase microextraction and liquid chromatography

A new approach to the rapid determination of amoxicillin (AMO) in human plasma followed by solid phase microextraction (SPME) fiber coatings based on conducting polymers (polypyrrole and polythiophene) and high performance liquid chromatography (HPLC) has been described. The porous structures of the electrochemically deposited polymer coatings have been characterized by scanning electron microscopy (SEM). The experimental parameters relating to the extraction efficiency of the SPME fibers such as pH, extraction time and desorption conditions (solvents, time) were studied and selected. The SPME/HPLC-UV method was linear over a working range of 1-50 μg ml(-1). The inter-day accuracy (expressed as coefficients of variations, CVs) was less than 15% and precision (expressed as the relative standard deviations, RSDs) with percentage values was less than 5.9%. Amoxicillin was found to be stable in the human plasma at room temperature (20 °C) within 8 hours. The developed method was successfully applied to the analysis of real human plasma samples. The limit of detection and limit of quantification for amoxicillin in plasma were 1.21 μg ml(-1) and 3.48 μg ml(-1), respectively.     

Comparing ab initio density-functional and wave function theories: the impact of correlation on the electronic density and the role of the correlation potential

The framework of ab initio density-functional theory (DFT) has been introduced as a way to provide a seamless connection between the Kohn-Sham (KS) formulation of DFT and wave-function based ab initio approaches [R. J. Bartlett, I. Grabowski, S. Hirata, and S. Ivanov, J. Chem. Phys. 122, 034104 (2005)]. Recently, an analysis of the impact of dynamical correlation effects on the density of the neon atom was presented [K. Jankowski, K. Nowakowski, I. Grabowski, and J. Wasilewski, J. Chem. Phys. 130, 164102 (2009)], contrasting the behaviour for a variety of standard density functionals with that of ab initio approaches based on second-order M?ller-Plesset (MP2) and coupled cluster theories at the singles-doubles (CCSD) and singles-doubles perturbative triples [CCSD(T)] levels. In the present work, we consider ab initio density functionals based on second-order many-body perturbation theory and coupled cluster perturbation theory in a similar manner, for a range of small atomic and molecular systems. For comparison, we also consider results obtained from MP2, CCSD, and CCSD(T) calculations. In addition to this density based analysis, we determine the KS correlation potentials corresponding to these densities and compare them with those obtained for a range of ab initio density functionals via the optimized effective potential method. The correlation energies, densities, and potentials calculated using ab initio DFT display a similar systematic behaviour to those derived from electronic densities calculated using ab initio wave function theories. In contrast, typical explicit density functionals for the correlation energy, such as VWN5 and LYP, do not show behaviour consistent with this picture of dynamical correlation, although they may provide some degree of correction for already erroneous explicitly density-dependent exchange-only functionals. The results presented here using orbital dependent ab initio density functionals show that they provide a treatment of exchange and correlation contributions within the KS framework that is more consistent with traditional ab initio wave function based methods.     

Means of iterates

Aequationes mathematicae - We determine continuous bijections f, acting on a real interval into itself, whose k-fold iterate is the quasi-arithmetic mean of all its subsequent iterates from $$f^0$$...     

Porosity and the L p -conjecture

Recently, Abtahi, Nasr-Isfahani, and Rejali [1] have shown that if G is a locally compact but not compact topological group and p > 2, then there are two functions, f and g, such that the convolution f*g{f\star g} is equal to ∞ on some set of positive measure. In the paper we show the nonexistence of f*g{f\star g} on a set of positive measure for (f, g) from a complement of a σ-porous set.     

Functional Central Limit Theorem for Additive Functionals of <Emphasis Type="Italic">α</Emphasis>-stable Processes

Let β be a standard Brownian motion, let X be an α-stable process, and let f=[^(m)]f=\widehat \mu be the Fourier transform of a discrete measure. It is shown that weakly in C([0, + ∞ )),

Time irregularity of generalized Ornstein–Uhlenbeck processes

This Note is concerned with the properties of solutions to a linear evolution equation perturbed by a cylindrical Lévy process. It turns out that solutions, under rather weak requirements, do not have a càdlàg modification. Some natural open questions are also stated.